The first named storm of the Atlantic hurricane season is posing an uncertain threat to the Gulf of Mexico, even as efforts to contain the worst oil spill in U.S. history are set to ramp up.

For now, Tropical Storm Alex, which is hitting the western Caribbean with rain and high winds, is not expected to pass close to BP Plc.'s blown-out well off the Louisiana coast.

But even a miss that only generates large waves could greatly complicate clean-up efforts from Louisiana to Florida.

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Current official estimates suggest between 35,000 to 60,000 barrels a day are leaking from the rogue well. BP collected over 24,000 barrels on Friday and about 11,640 barrels in the first half of Saturday, the company estimated.

New equipment being moved to the site of the leak in the coming week could raise the daily collection rate to 53,000 barrels a day, U.S. Coast Guard Admiral Thad Allen, who is coordinating the U.S. oil spill response, said on Saturday.

U.S. Energy Secretary Steven Chu and Interior Secretary Kenneth Salazar are also scheduled to review plans on Wednesday for a new containment system that could boost collection to 80,000 barrels per day, Allen said.

The ultimate solution to plugging the undersea gusher still lies in a relief well being drilled by BP. On Friday, the company said drilling is on track to intercept the blown well.

But progress could be scuttled if Alex, or a subsequent storm, comes too close to the leak site.

Allen said BP would be forced to evacuate the vessels and personnel working to contain the spill if a storm with gale-force winds, 39 miles per hour or stronger, were expected within five days at the leak site. That would once again leave the well gushing uncontrollably.

For now, Alex does not pose such a risk -- a rare piece of good news for the unprecedented oil spill disaster now in its 69th day. "We understand it's moving westerly at this time and does not threaten the site," said Allen.